No. You probably thinking some other vaccine and infection, not covid. For covid once infected, vaccinated people express similar number of virus in their saliva as unvaccinated (see for example [1]). Additionally, infected vaccinated people have lower intensity symptoms or now symptoms at all, and thus more likely to go about their business as usual (and thus spread the virus) than to stay home like unvaccinated. As a result the vaccinated people do possibly spread more infection than unvaccinated. The obviously propagandistic and using government force push "do it for the good of the community" (very USSR style) for covid vaccinations against the science - as those results were already known at the end of 2021 - drove a lot of new people into vaccine-sceptic crowd.
[1] https://www.ucdavis.edu/health/covid-19/news/viral-loads-sim...
"new study from the University of California, Davis, Genome Center, UC San Francisco and the Chan Zuckerberg Biohub shows no significant difference in viral load between vaccinated and unvaccinated people who tested positive for the delta variant of SARS-CoV-2. It also found no significant difference between infected people with or without symptoms.
...
Although vaccinated people with a breakthrough infection are much less likely to become severely ill than unvaccinated, the new study shows that they can be carrying similar amounts of virus and could potentially spread the virus to other people."
